The nonconforming virtual element method for fourth-order singular perturbation problem

2020 ◽  
Vol 46 (2) ◽  
Author(s):  
Bei Zhang ◽  
Jikun Zhao ◽  
Shaochun Chen
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Singular Perturbation Problem ◽  
Virtual Element Method ◽  
Perturbation Problem ◽  
Virtual Element ◽  
Element Method

AC0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem

2018 ◽  
Vol 52 (5) ◽  
pp. 1981-2001 ◽  
Author(s):  
Yuan Bao ◽  
Zhaoliang Meng ◽  
Zhongxuan Luo
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Degrees Of Freedom ◽  
Perturbation Parameter ◽  
Singular Perturbation Problem ◽  
Mean Values ◽  
Perturbation Problem ◽  
Convex Quadrilateral ◽  
The Mean ◽  
Quadrilateral Finite Element

In this paper, aC0nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateralQ, the shape function space is the union ofS21(Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.

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